The Shapley Value and Related Solution Concepts

Abstract

The Shapley value not only belongs to the most important solution concepts of cooperative game theory but it is also an easily tractable mathematical object with a remarkably wide range of applications. After necessary preliminaries, we introduce basic properties and characterizations of the Shapley value for cooperative games with transferable utility. Then we deal with some of its extensions appearing frequently in the literature. In particular, we present the Aumann–Drèze and Owen generalizations to games with a coalition structure, and the Myerson extension to games with a graph structure. We conclude with the probabilistic values and a brief discussion of application to cost allocation problems.